基于CIR随机利率模型下期权定价的实证研究

Demonstration of Option Pricing Based on the CIR Stochastic Interest Rate Model

考虑当标的资产的价格过程服从几何布朗运动,并且利率过程满足均值回复的CIR过程时,欧式期权的定价问题.利用Δ-对冲和测度变换的鞅方法,推导出欧式期权的解析形式的闭式解.此外,用Monte Carlo方法求出期权数值解.同时,对比了数值解和解析解之间的不同.

The pricing of European options is considered in the case that the underlying asset price follows the geometric Brownian motion with the stochastic rate process being the mean revers- ing process, CIR process. By applying the methods of A- hedging and equivalent martingale, i. e. , numeraire exchange,the closed form of pricing formulas is obtained. Furthermore a, Monte Carlo simulation is used to compute the numerical solution. Then the errors between these two solutions is compared.